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To cause a lot of problems. Termites have wreaked havoc on the structural integrity of our house, unfortunately.
play havoc with (someone or something)
To cause issues or disruptions for someone or something. The road closures have played havoc with rush-hour traffic. This humidity is going to play havoc with my hair.
wreak havoc (with something)
to cause a lot of trouble with something; to ruin or damage something. Your bad attitude will wreak havoc with my project. The rainy weather wreaked havoc with our picnic plans.
wreak something (up)on someone or something
to cause damage, havoc, or destruction to someone or something. (Upon is formal and less commonly used than on.) The storm wreaked destruction upon the little village. It wreaked much havoc on us.
wreak vengeance (up)on someone or something
Cliché to seek and get revenge on someone by harming someone or something. The gangster wreaked his vengeance by destroying his rival's house. The general wanted to wreak vengeance on the opposing army for their recent successful attack.
Also, raise or wreak havoc . Disrupt, damage, or destroy something, as in The wind played havoc with her hair, or The fire alarm raised havoc with the children, or The earthquake wrought havoc in the town. The noun havoc was once used as a command for invaders to begin looting and killing, but by the 1800s the term was being used for somewhat less aggressive activities. For a synonym, see play the devil with.